C1 chapter 4 - sketching curves

In this chapter you will learn how to sketch, interpret and translate polynomial and reciprocal graphs .

C1 § 4.1 cubic in factors

You need to be able to: plot cubic graphs given in factor form.
Explore the effect of changing the factors with this Desmos interactive:

You need to know: that the values in the brackets predict the roots (UK English) or zeros (US English) of the function.

The cubic

$y = (x - a)(x - b)(x - c)$

has roots or zeros at

$x = a \text {, } x = b \text { and } x = c$

Examples:

C1 Exercise 4A

• C1 Exercise 4A worked solutions:
• 

  C1 Exercise 4A (sketching cubics).jnt
  

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  C1 Exercise 4A (sketching cubics).pdf
  

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• these solutions are incomplete, but it's quite a straightforward exercise. If you need solutions to any questions I haven't yet done, please request them on the Sandbox
  
  
• Questions similar to this exercise:

C1 § 4.2 a binomial cubed

You need to already know: the shape of cubic functions determined by their factors (above)
You are learning to: sketch and interpret graphs of the form y = ±(x - k)³

Explore this class of cubic functions with the interactive:


You will discover that:

C1 section 4.2 (binomial cubed).jnt

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C1 section 4-2 (binomial cubed).pdf

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• 60 KB

C1 Exercise 4B

• C1 Exercise 4B worked solutions:
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